A precise measurement of the cross section of the process e(+)e(-)->pi(+)pi(-)(gamma) from threshold to an energy of 3 GeV is obtained with the initial state radiation (ISR) method using 232 fb(-1) of data collected with the BABAR detector at e(+)e(-) center-of-mass energies near 10.6 GeV. The ISR luminosity is determined from a study of the leptonic process e(+)e(-)->mu(+)mu(-)gamma(gamma). The leading-order hadronic contribution to the muon magnetic anomaly calculated using the pi pi cross section measured from threshold to 1.8 GeV is (514.1 +/- 2.2(stat)+/- 3.1(syst))x10(-10).